Recent works [1]}, [2]} have established the connections between many feature aggregation operations in representative GNNs and a graph signal denoising problem with Laplacian regularization. Here, we only introduce GCN/SGC as an examples to show the connection from a perspective of graph signal denoising. The more discussions are elaborated in Appendix . Feature aggregation in Graph Convolutional Network (GCN) or Simplifying Graph Convolutional Network (SGC) is given by \(\mathbf {X}_{agg}=\tilde{\mathbf {A}}\mathbf {X}_{trans}\) , where \(\tilde{\mathbf {A}}=\tilde{\mathbf {D}}^{-\frac{1}{2}}\hat{\mathbf {A}}\tilde{\mathbf {D}}^{-\frac{1}{2}}\)  is a normalized self-loop adjacency matrix \(\hat{\mathbf {A}}=\mathbf {A}+\mathbf {I}\) , and \(\tilde{\mathbf {D}}\)  is degree matrix of \(\tilde{\mathbf {A}}\) . Recent works [1]}, [2]} provably demonstrate that such feature aggregation is equivalent to one-step gradient descent to minimize \(tr(\mathbf {F}^{\top }\big (\mathbf {I}-\tilde{\mathbf {A}})\mathbf {F}\big )\)  with initialization \(\mathbf {F}=\mathbf {X}_{trans}\) .
